Candidates for nonzero Betti numbers of monomial ideals

Let I be a monomial ideal in the polynomial ring S generated by elements of degree at most d. In this paper, it is shown that, if the i-th syzygy of I has no elements of degrees j,…,j+(d?1) (where j≥i+d), then (i+1)-th syzygy of I does not have any element of degree j+d. Then we give several applications of this result, including an alternative proof for Green–Lazarsfeld index of the edge ideals of graphs as well as an alternative proof for Fröberg’s theorem on classification of square-free monomial ideals generated in degree 2 with linear resolution. Among all, we deduce a partial result on subadditivity of the syzygies for monomial ideals.     

Well‐posedness of initial boundary value problems on longitudinal impact on a composite linear viscoelastic bar

We investigate the correctness of the initial boundary value problem of longitudinal impact on a piecewise‐homogeneous semi‐infinite bar consisting of a semi‐infinite elastic part and finite length visco‐elastic part whose hereditary properties are described by linear integral relations with an arbitrary difference kernel. Introducing nonstationary regularization in boundary conditions and in the contact conditions, the well‐posedness of the considered problem is proved. Copyright © 2017 John Wiley & Sons, Ltd.     

A polyaniline-magnetite nanocomposite as an anion exchange sorbent for solid-phase extraction of chromium(VI) ions

This work describes a novel polyaniline-magnetite nanocomposite and its application to the preconcentration of Cr(VI) anions. The material was obtained by oxidative polymerization of aniline in the presence of magnetite nanoparticles. The parameters affecting preconcentration were optimized by a Box-Behnken design through response surface methodology. Extraction time, amount of magnetic sorbent and pH value were selected as the main factors affecting sorption. The sorption capacity of the sorbent for Cr(VI) is 54 mg g⁻¹. The type, volume and concentration of the eluents, and the elution time were selected as main factors in the optimization study of the elution step. Following sorption and elution, the Cr(VI) ions were reacted with diphenylcarbazide, and the resulting dye was quantified by HPLC with optical detection at 546 nm. The limit of detection is 0.1 μg L⁻¹, and all the relative standard deviations are <6.3 %. The nanocomposite was successfully applied to the rapid extraction and determination of trace quantities of Cr(VI) ions in spiked water samples.

A schematic procedure of magnetic solid phase extraction

     

A polyaniline-magnetite nanocomposite as an anion exchange sorbent for solid-phase extraction of chromium(VI) ions

This work describes a novel polyaniline-magnetite nanocomposite and its application to the preconcentration of Cr(VI) anions. The material was obtained by oxidative polymerization of aniline in the presence of magnetite nanoparticles. The parameters affecting preconcentration were optimized by a Box-Behnken design through response surface methodology. Extraction time, amount of magnetic sorbent and pH value were selected as the main factors affecting sorption. The sorption capacity of the sorbent for Cr(VI) is 54 mg g^?1. The type, volume and concentration of the eluents, and the elution time were selected as main factors in the optimization study of the elution step. Following sorption and elution, the Cr(VI) ions were reacted with diphenylcarbazide, and the resulting dye was quantified by HPLC with optical detection at 546 nm. The limit of detection is 0.1 μg L^?1, and all the relative standard deviations are <6.3 %. The nanocomposite was successfully applied to the rapid extraction and determination of trace quantities of Cr(VI) ions in spiked water samples. Figure

A schematic procedure of magnetic solid phase extraction     

Synthesis and application of a thermosensitive tri-block copolymer as an efficient sample treatment technique for preconcentration and ultra-trace detection of lead ions

We have designed and synthesized a thermosensitive tri-block copolymer for selective trace extraction of Pb(II) ions from biological and food samples. The polymer was characterized by Fourier transform IR and NMR spectroscopy, and by gel permeation chromatography. The critical aggregation concentration and lower critical solution temperature were determined via fluorescence and UV spectrophotometry, respectively. The effects of solution pH value, amount of copolymer, of the temperature on extraction and on phase separation, and of the matrix on the extraction of Pb(II) were optimized. Pb(II) ions were then quantified by FAAS. The use of this copolymer resulted in excellent figures of merit including a calibration plot extending from 0.5 to 160 μg L^?1 (with an R² of >0.99), a limit of detection (LOD) as low as 90 pg L^?1, an extraction efficiency of >98 %, and relative standard deviations of <4 % for eight separate extraction experiments.

Optical and electrochemical DNA nanobiosensors

In the past two decades, nanoscale advanced materials have been explored for biosensing molecules, so new horizons have opened up for identifying and quantifying biomolecules, and possible early diagnosis of diseases.DNA nanobiosensors show promise. This article provides an overview on their optical and electrochemical aspects. We discuss recent progress in this field, describing basic concepts of molecular beacons and quantum dots as optical nano-imaging systems. Also, carbon nanotubes provide a platform for development and advancement of electrochemical DNA nanobiosensors, which are increasingly being implemented as robust tools for detection in biomedical sciences.     

Online thorium determination after preconcentration in a minicolumn having XAD-4 resin impregnated with N-benzoylphenylhydroxylamine by FI-spectrophotometry

A very sensitive and selective flow injection on-line determination method of thorium (IV) after preconcentration in a minicolumn having XAD-4 resin impregnated with N-benzoylphenylhydroxylamine is described. Thorium (IV) was selectively adsorbed from aqueous solution of pH 4.5 in a minicolumn at a flow rate of 13.6 mL min^?1, eluted with 3.6 mol dm^?3 HCl (5.6 mL min^?1), mixed with arsenazo-III (0.05% in 3.6 mol dm^?3 HCl stabilized with 1% Triton X-100, 5.6 mL min^?1) at confluence point and taken to the flow through cell of spectrophotometer where its absorbance was measured at 660 nm. Peak height was used for data analyses. The preconcentration factors obtained were 32 and 162, detection limits of 0.76 and 0.150 ??g L^?1, sample throughputs of 40 and 11 h^?1 for preconcentration times of 60 and 300 s, respectively. The tolerance levels for Zr(IV) and U(VI) metal ions is increased to 50-folds higher concentration to Th(IV). The proposed method was applied on different spiked tap water, sea water and biological sample and good recovery was obtained. The method was also applied on certified reference material IAEA-SL1 (Lake Sediment) for the determination of thorium and the results were in good agreement with the reported value.     

Synthesis,spectroscopy, and X-ray crystal structures of copper(II) complexes of the tridentate ONS ligand formed by condensation of 4,4,4-trifluoro-1-(2-thienyl)-2,4-butanedione with S-benzyldithiocarbazate

A new tridentate ONS ligand, H₂L, has been synthesized by condensing thenoyltrifluoroacetone(4,4,4-trifluoro-1-(2-thienyl)-2,4butaneanedione) with S-benzyldithiocarbazate and its structure determined by X-ray diffraction. In the solid state, the Schiff base exists as the ketoamine-thioketo tautomer but in solution and in the presence of copper(II), it converts to the enol-thiol form and deprotonates to give copper(II) complexes of formula, [CuL] and [CuLL¹] (L = doubly deprotonated form of the ligand; L¹ = py, bipy or phen] which have been characterized by magnetic, spectroscopic, and X-ray diffraction studies. An X-ray crystallographic analysis shows that [CuL(py)] has a square-planar geometry with the ligand coordinated to the copper(II) center via the enolate oxygen, the azomethinic nitrogen and the thiolate sulfur, the fourth coordination position being occupied by pyridine. The [CuL(bipy)] complex is five-coordinate with a structure close to square-pyramidal in which the Schiff base acts as a doubly deprotonated tridentate ONS ligand and bipy is bidentate.     

Optimization of carrier-mediated three-phase hollow fiber microextraction combined with HPLC-UV for determination of propylthiouracil in biological samples

Carrier-mediated three-phase hollow fiber microextraction combined with high-performance liquid chromatography-ultra violet detection (HPLC-UV) was applied for the extraction and determination of propylthiouracil in biological samples. Propylthiouracil (PTU) was extracted from 7.5 mL of the basic solution (the source phase) with pH 12 into an organic phase (n-octanol containing 6% (w/v) of Aliquat 336 as the carrier) impregnated in the pores of a hollow fiber, and finally was back extracted into 24 μL of the acidic solution located inside the lumen of the hollow fiber (the receiving phase). The extraction was performed through the gradient of counter ion from the source to the receiving phase. The effects of different variables on the extraction efficiency were studied simultaneously using an experimental design. A half-fractional factorial design was employed for screening to determine the variables significantly affecting the extraction efficiency. Then, the factors with significant effect were optimized using a central composite design (CCD) and the response surface equations were developed. The optimal experimental conditions obtained from this statistical evaluation included: source phase, pH 12; temperature, 25 °C; extraction time, 40 min; counter ion concentration, 2 mol L⁻¹ of NaClO₄; organic solvent 6% of Aliquat in octanol and without salt addition in the source phase. Under the optimized conditions, the preconcentration factors were between 125 and 198 and also the limit of detections (LODs) ranged from 0.1 μg L⁻¹ to 0.4 μg L⁻¹ in different biological samples. The calibration curve was linear (r² = 0.998) in the concentration range of 0.5-1000 μg L⁻¹. Finally, the feasibility of the proposed method was successfully confirmed by extraction and determination of PTU in human plasma and urine as well as the bovine milk and meat samples in microgram per liter, and suitable results were obtained (RSDs < 6.3%).